Adding the "Paranoid" trait would allow the player, when creating his character, to receive 6 points to choose a good trait or even 8.
This trait would make the character, as it says, paranoid, making he/she see and hear things that are not there like hearing a zombie knocking on the door, and even seeing the animation. The player can also hear a zombie behind him but there's nothing, hearing breaking windows, cars turning on, and so on...
Instead of being a bad character trait, it could be instead a feeling that the player develops after spending 7 days anxious, or even less. And once you become paranoid, it's hard to remove it.